Temperature Dependence of the Speed of Sound, Doppler Effect Homework #4

Speed of Sound in Room 910 Now. Temperature is 73 degrees F. (22.8 degrees Centigrade) Length of tube meters

Temperature Dependence of Speed of Sound: When sound travels through any ideal gas, there is a dependence of the speed of sound on the absolute temperature of the gas. The derivation of the formula is based on the wave traveling through the air as adiabatic expansions and compressions of the air molecules. The derivation is beyond the scope of the class. The result of the derivation is: The equation on the left requires an absolute temperature (in kelvins) and the equation on the right requires the temperature in degrees Celsius.

Example #1: What is the speed of sound if the temperature in a container is 22.8 °C?

Ex. #2: What is the temperature, in °C, in a container if the speed of sound is 312 m/s?

Ex. #3: A student determines that a standing sound wave has a wavelength of 78.4 cm and a frequency of 440 Hz. (a) What is the speed of sound in the air column carrying the standing sound wave?

(b) What is the temperature in the air column? From the derivation in problem #2, get:

The Doppler effect is the apparent shift of frequency of a sound produced by a source and heard by an observer when the source and/or the observer are moving relative to one another. If the source and the observer are moving towards one another, a frequency higher than normal is observed. If the source and observer are moving away from one another, a frequency lower than normal is observed. Automobile Car Horn

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The Doppler effect can be modeled by the following equation: f o = observed frequency, f s = source frequency, v = speed of sound, v o = speed of observer, v s = speed of source. How to choose the ±: If the source is moving in a direction pointing towards the observer, choose a (–) sign in the denominator. If the source is moving in a direction pointing away from the observer, choose a (+) sign in the denominator. If the observer is moving in a direction pointing towards the source, choose a (+) sign in the numerator. If the observer is moving in a direction pointing away from the source, choose a (–) sing in the numerator.

Ex. 4: A person standing at a bus bench hears a passing car honk its horn. The horn’s original frequency is 400 Hz and the car’s speed is 20.0 m/s. Assume the speed of sound is 345 m/s. What is the frequency heard by the observer if the car is approaching her position? Chose the (–) sign in the denominator if the source moves towards the observer.

Ex. 5: What is the frequency heard by the observer if the car is moving away from her position? Chose the (+) sign in the denominator if the source moves away from the observer.

Ex. 6: Mr. Heaton rides his bike along Dorothy Lane with a speed of 10.0 m/s. A car approaches from behind at 20.0 m/s and honks a 500 Hz horn. What is the frequency of the tone heard by Mr. Heaton? Assume the speed of sound is 345 m/s. car Mr. H Chose the (–) sign in the numerator if the observer moves away from the source. Chose the (–) sign in the denominator if the source moves towards the observer.

Ex. 7: What is the frequency heard by Mr. Heaton if the car continues to honk its horn after it passes him? Mr. Heaton Chose the (+) sign in the numerator if the observer moves towards the source. Chose the (+) sign in the denominator if the source moves away from the observer. car

Ex. #8: An observer on a train platform hears a train horn as a train passes his position. The frequency heard by the observer appears to drop one octave as the train passes. In other words, the frequency heard as the train approaches is twice the frequency heard as the train departs. What is the speed of the train if the speed of sound is 345 m/s? case I: train approaching train observer

case II: train departing train observer octave difference:

The (unknown) frequency of the source divides out:

Ex. 9: A speeding truck drives towards a stationary brick wall at 30.0 m/s. The confused driver honks his 444 Hz horn, hoping the wall will jump out of his way. What frequency will the driver hear for the sound reflected off of the wall? {Hint: First treat the wall as the observer and the truck as the source. Determine the frequency “heard” by the wall. This frequency is then reflected back to the truck by the wall, so next make the wall the source and the truck the observer.} truck wall

Next let the wall be the source and the truck the observer. truck wall